摘要
精确高效地预测高耸结构动力特性是结构设计的关键问题之一。针对高耸结构的动力特性展开研究工作:首先,根据高耸结构的特点,基于结构动力学原理推导了连续的动力微分方程;在此基础上,通过平均等效、坐标变换和无量纲归一化等方法对无阻尼自由振动的偏微分方程进行了简化;随后采用Adomian分解法(Adomian Decomposition Method,ADM)对无量纲振型进行分解,并引入边界条件和连续条件求解了模态频率和模态振型;最后,以某高耸钢烟囱为例进行了数值模拟,研究了ADM的收敛性,并与实测、有限单元法、集中质量法的结果进行了比较。结果表明:当Adomian分解阶数M取为8时,即可满足工程需要;对于典型的分段高耸结构,ADM相较于其他方法具有更高的精度。因此,该方法可以用于高耸结构的动力特性分析,并具有较高的精度和效率。
It is one of the key issues to predict the dynamic characteristics accurately and efficiently for the design of high-rise buildings.The research of this paper is aiming at solving the dynamic characteristics of high-rise buildings.Firstly,the dynamic differential equation of high-rise buildings is derived on the basis of mechanics of structural dynamics.Secondly,the equation is simplified by some mathematical methods including average equivalence,coordinate transformation and dimensionless method.And the dimensionless modal shape is decomposed using Adomian decomposition method （ADM）,together with the boundary conditions and continuity conditions,the modal frequencies and modal shapes are obtained.Lastly,the dynamic characteristics of a high-rise chimney is calculated following the procedure,and the results are compared with those of field test and other methods such as finite element method and lumped mass method.The results show that if the summation limit M of the Adomian decomposition series reaches 8,the accuracy requirement in engineering can be satisfied,and comparing with other two methods,ADM is more accurate for piecewise linear high-rise buildings.Therefore,this method offers an accurate and effective method of dynamic analysis of high-rise buildings.
出处
《振动工程学报》
EI
CSCD
北大核心
2013年第4期493-499,共7页
Journal of Vibration Engineering
基金
国家杰出青年基金资助项目(50725858)
东南大学优秀博士论文基金资助项目(YBJJ1006)
关键词
高耸结构
动力特性
ADOMIAN分解法
钢烟囱
high-rise buildings
dynamic characteristic
Adomian decomposition method
steel chimney
